Stability by averaging of linear discrete-time systems

Adam Jbara, Rami Katz, Emilia Fridman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Recently, a constructive approach to averaging-based stability was proposed for linear continuous-time systems with small parameter ϵ > 0 and rapidly-varying almost periodic coefficients. The present paper extends this approach to discrete-time linear systems with rapidly-varying periodic coefficients. We consider linear systems with state delays, where results on the stability via averaging are missing. Differently from the continuous-time, our linear matrix inequalities (LMIs) are feasible for any delay (i.e. the system is exponentially stable) provided E is small enough. We introduce an efficient change of variables that leads to a perturbed averaged system, and employ Lyapunov analysis to derive LMIs for finding maximum values of the small parameter ϵ > 0 and delay that guarantee the exponential stability. Numerical example illustrates the effectiveness of the proposed approach.

Original languageEnglish
Title of host publication2024 European Control Conference, ECC 2024
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1662-1667
Number of pages6
ISBN (Electronic)9783907144107
DOIs
StatePublished - 2024
Event2024 European Control Conference, ECC 2024 - Stockholm, Sweden
Duration: 25 Jun 202428 Jun 2024

Publication series

Name2024 European Control Conference, ECC 2024

Conference

Conference2024 European Control Conference, ECC 2024
Country/TerritorySweden
CityStockholm
Period25/06/2428/06/24

Funding

FundersFunder number
Tel Aviv University
Israel Science Foundation673/19
ISF-NSFC3054/23

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